She fainted from fear.

Literal

She [topic-は] fear [from-で] fainted.

失神 ('faint, lose consciousness') is the medical/clinical term — 気絶 is more colloquial. Both work fine in everyday usage, but 失神 has a slight clinical detachment. The で here is causal — the fear is the reason for the faint. Built compactly: 失 ('lose') + 神 ('spirit, mind') = 'lose one's spirit/consciousness.' The kanji choices in Japanese medical/psychological vocabulary often expose old folk-psychology models.